Don't know if this newspaper transcript (below) is any help (found by Eilleen).
I've also found some Cockin's linked to the following places:-
A George Cockin of Sandholme, in the Parish of Eastrington, sold the property in 1824 and moved to Clementhorpe.
Huddersfield.
Leeds & Hull Missionary Meetings in Hull Packet of 17 August 1813 involving a Mr Cockin, Joseph Cockin and Rev. John Cockin.
Haifax.
Luddington in Lincolnshire.
Hull Daily Mail of 9th April 1908
FOCKERBY.
DEATH.- By the death of Mr William Cockin
at the advanced age of 79 Fockerby loses one of
its most familiar figures. Mr Cockin is the last
of that name residing in the village, the family
living on the same homestead for upwards of 100
years. The deceased was a considerable pro-
perty owner, having property in Garthorpe,
Eastoft, Luddington and Adlingfleet. His wife
having pre-deceased him, and having no child-
ren, the nearest relatives to mourn his loss are
nieces and nephews. The funeral took place at
Adlingfleet, and was conducted by the Rev. A. T.
Ryan, assisted by Captain Cunliffe, C.A.
EDIT: I have also found out a GRO Birth Certificate for a later (obviously much too late for 1815), but it might help tracing backward ...
Registration District SELBY
BIRTH in the Sub-district of SNAITH
16th September 1837 for Jane;
William Cockin Father Labourer, Cowick;
Mother Ann Cockin formerly Robinson
Any suggestions of a Jane Cockin existing in 1815 and old enough to sign as a Witness, please?